Solve for $x$ and $y$ using substitution. ${2x-5y = -11}$ ${y = 5x-7}$
Solution: Since $y$ has already been solved for, substitute $5x-7$ for $y$ in the first equation. ${2x - 5}{(5x-7)}{= -11}$ Simplify and solve for $x$ $2x-25x + 35 = -11$ $-23x+35 = -11$ $-23x+35{-35} = -11{-35}$ $-23x = -46$ $\dfrac{-23x}{{-23}} = \dfrac{-46}{{-23}}$ ${x = 2}$ Now that you know ${x = 2}$ , plug it back into $\thinspace {y = 5x-7}\thinspace$ to find $y$ ${y = 5}{(2)}{ - 7}$ $y = 10 - 7$ $y = 3$ You can also plug ${x = 2}$ into $\thinspace {2x-5y = -11}\thinspace$ and get the same answer for $y$ : ${2}{(2)}{ - 5y = -11}$ ${y = 3}$